Fixed typesetting in footnotes, but they are so dense that the project no longer compiles in overleaf :(

1 files changed, 19 insertions, 22 deletions

diff --git a/papers/2.tex b/papers/2.tex
index 620bcc4..4fd42b0 100644
--- a/papers/2.tex
+++ b/papers/2.tex
@@ -693,7 +693,7 @@ realize, per tolerance, that you cannot tell the difference between the
 two cases. In effect, you must conclude that one of the cases was
 falsely classified when you made the division in the previous period.
 Thus, your p-set changes. Therefore, the very considering of the sharp
-distinction would automatically progress us to t+1, ensuring that there
+distinction would automatically progress us to $t+1$, ensuring that there
 was no sharp boundary. In conclusion, the fixed time objection is not a
 significant worry to the dynamic view.
 
@@ -717,40 +717,40 @@ In what follows, I will defend the dynamic view from this objection. See
 footnotes for background on contextualism\footnote{Contextualism rests
   on the claim that vagueness is a species of context-sensitivity. This
   roughly means that, in its application across different contextual
-  circumstances, a vague term maintains a constant \emph{character} but
-  shifts in \emph{content}. Therefore, vague terms function like
+  circumstances, a vague term maintains a constant \textit{character} but
+  shifts in \textit{content}. Therefore, vague terms function like
   indexical terms. The relationship of vagueness and indexicality is a
   contested matter for contextualists. Some hold that vague terms behave
-  \emph{like} indexicals, while others claim they \emph{are} indexicals.
+  \textit{like} indexicals, while others claim they \textit{are} indexicals.
   However, this distinction is not directly relevant to the discussion,
   and the objections raised here apply equally to both views. Consider
-  the word \emph{now}. It adheres to the same grammatical rules (i.e.,
-  has the same \emph{character}) when uttered today and tomorrow.
+  the word \textit{now}. It adheres to the same grammatical rules (i.e.,
+  has the same \textit{character}) when uttered today and tomorrow.
   However, when said today, it picks out a different time than it does
-  when used tomorrow (i.e., has different \emph{content}). Similarly, a
-  vague predicate like \emph{tall} is used in the same way when applied
+  when used tomorrow (i.e., has different \textit{content}). Similarly, a
+  vague predicate like \textit{tall} is used in the same way when applied
   to members of a group of pygmy peoples, as when applied to a group of
   Dutch people. However, it would pick out radically different people.
-  In the first case, the extension of \emph{tall} likely includes some
+  In the first case, the extension of \textit{tall} likely includes some
   of the world's shortest people; in the second, some of the tallest.
-  See Roy Sorensen, ``Vagueness,'' \emph{The Stanford Encyclopedia of
+  See Roy Sorensen, ``Vagueness,'' \textit{The Stanford Encyclopedia of
   Philosophy} (Winter 2023 Edition), ed. Edward N. Zalta and Uri
   Nodelman,
   \url{https://plato.stanford.edu/archives/win2023/entries/vagueness/}.}
-and their solution to the Sorites\footnote{Contextualists exploit this
+and their solution to the Sorites.\footnote{Contextualists exploit this
   idea of unstable extensions over contexts to solve the Sorites by
   accusing it of equivocating different meanings of a vague term.
   Similarly to the supervaluationists, the contextualists target the
   inductive premise (2). The contextualist is committed to the claim of
   weak tolerance (WT), which states that when two members of a bordering
-  pair are considered in the same context C, they will belong to the
+  pair are considered in the same context $C$, they will belong to the
   same extension. However, WT permits that when one member is considered
-  in context C and the other in C', then they might belong to a
+  in context $C$ and the other in $C'$, then they might belong to a
   different extension. See Jonas Åkerman and Patrick Greenough, "Hold
-  the Context Fixed---Vagueness Still Remains," in \emph{Relative
+  the Context Fixed---Vagueness Still Remains," in \textit{Relative
   Truth}, ed. Manuel García-Carpintero and Max Kölbel (Oxford University
   Press, 2010), 275--76,
-  \href{https://doi.org/10.1093/acprof:oso/9780199570386.003.0016}.
+  \url{https://doi.org/10.1093/acprof:oso/9780199570386.003.0016}.
 
   The WT explains why the inductive premise seems to hold. If we
   consider any pair in the series, we will conclude that both members
@@ -759,13 +759,10 @@ and their solution to the Sorites\footnote{Contextualists exploit this
   fact, the context will gradually change across the series. This means
   that even if we classify neighbouring terms the same at first, this
   classification will not persist throughout the series. Thus, the
-  inductive premise of the sorites, such as `if n is short, then n+1 is
-  short', fails since the meaning of `short' is not the same for every
-  member \emph{n}. This is because, the shift of context C into C',
-  enables cases where `n is short' is true (in C) but `n+1 is short' is
-  false (in C'). See J. Åkerman, "Contextualist Theories of Vagueness,"
-  \emph{Philosophy Compass} 7 (2012): 470--75,
-  \href{https://doi.org/10.1111/j.1747-9991.2012.00495.x}.}.
+  inductive premise of the sorites, such as `if $\mathbf{n}$ is short, then $\mathbf{n}+1$ is short', fails since the meaning of `short' is not the same for every
+  member $\mathbf{n}$. This is because, the shift of context $C$ into $C'$,
+  enables cases where `$\mathbf{n}$ is short' is true (in $C$) but `$\mathbf{n}+1$ is short' is false (in $C'$). See J. Åkerman, "Contextualist Theories of Vagueness,"
+  \textit{Philosophy Compass} 7 (2012): 470--75, \url{https://doi.org/10.1111/j.1747-9991.2012.00495.x}.}
 The first point that I address is the idea that supervaluation is
 obsolete. On this view, its role at the first level could be replaced by
 the context-reminiscent p-sets. The intuitive idea is that, since shifty